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Both these ultrasonic range modules are fairly cheap modules, expect the HY-SRF05 to be the more expensive of the these two.

At a quick glance there are only small differences between these two:

HC-SR04

HY-SRF05

Working Voltage

5 VDC

5 VDC

Static current

< 2mA

<2 mA

Output signal:

Electric frequency signal, high level 5V, low level 0V

Electric frequency signal, high level 5V, low level 0V

Sensor angle

< 15 degrees

< 15 degrees

Detection distance (claimed)

2cm-450cm

2cm-450cm

precision

~3 mm

~2 mm

Input trigger signal

10us TTL impulse

10us TTL impulse

Echo signal

output TTL PWL signal

output TTL PWL signal

Pins

VCC

trig(T)

echo(R)

GND

VCC

trig(T)

echo(R)

OUT

GND

Not sure what the out pin is about, I have seen claims that it goes high when it detects a obstacle.
From my personal observations the HY-SRF05 seems like a slightly more accurate sensor and seems to have a much better range [I even got it to measure beyond the 4.5 meters it claims] – but if I were to build for instance a robot that should not collide with a wall that would not matter.

In short a ultrasonic sensor like this works like:

Send a pulse signal to I/O TRIG which is at least 10us long, this will activate the module to start detecting

The ultrasonic module will automatically send eight 40khz square waves, and will automatically detect when there is a reflect signal;

When there is an reflect signal back, the ECHO I/O will output a high level, the duration of the high-level signal is the time from untral sonic launch to return. As a result, the Measured distance = (T(Time of High Level output ) * (340M / S)) / 2 The reason for the division by two is that since this is a echo it has traveled both to and from the object. Note the speed of sound is dependent of the temperature so keep that in mind if you need accuracy

And something that I noticed is very important is the quality of the 5V I got from my USB port when the Arduino was hooked up. At first I got a very noisy signal that was only able to detect ranges of about 10 cm, but after I swapped the connection to not use a usb-hub the results were much better.

And to finish off here comes a bit more about how to calculate the distance based on the time for the sound: